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_ NASA TECHNICAL NASATMX-62,490_* MEMC,RANDUF_.

A DESIGN METHOD FOR ENTRANCE SECTIONS OF TRANSONIC

WIND TUNNELS WITH RECTANGULAR CROSS SECTIONS

Lionel L. Levy, Jr. and John B. McDevitt

Ames Resem_ Center __a"Moffett Field, Celif. 94035

(.AsA-_.-x-62490) A _szG..ET.OD Fo_ ,76-11o_IeANsosxc w_.D _U..eLS RE_IVED-

ENTRANCE SECTIOH5 OFWITH RBCTANGULka CROSS SECTIONS (N&Sk) 36 P ._- F_...c s_.oo CSCL1.e oucZds I_,vre_._.__rv

Sep_mber 1975

1976003957

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1. ReportNo. ] 2. GovemmantAccemionNo. 3. Rec_ent'sCatalogNo.

/

_M X-62,4_0 i4. Title lind _l_itle 5. Report Date

A DESIGN METHOD FOR ENTRANCE SECTIONS OF TRANSONIC

Wl_l_) 'I[J'_ELS _1'1_ RECTANGULAR CROSS SECTIONS 6. Performing OrpnizationCodeA-6293

7. Author(s) 8. P_forrni_ Orglnization R_rt No.

Lionel L. Levy, Jr. and John B. McDevitt

10. Work Unit No.

O._Ommlmhm _m_ md _ 505-06-13

NASA Ames Research Center 11.Con_ ore,,tNo.

Moffett Field, Calif. 9403513. Type of Report and Perk)d Covlred

12. ,_,,_t_' _ _ and_ Technical Memorandum

National Aeronautics and Space Administration 14.s_om_i_ _ Cod.

Washington, D. C. 20546

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A technique has been developed to design entrance sections for transonic

or high-speed subsonic wind tunnels with rectangular cross sections which

satisfies two important requirements: (i) the transition from a circular

cross-section settling chamber to a rectangular test section is accomplished

smoothly so as not to introdace secondary flows (vortices or boundary-layer

separation) into a uniform =est stream and (2) the transition is accomplished

within a specified length. The mathematical technique for shaping the

entrance section is described and the results of static-prcssure measurements

In the transition region and of static- and total-pressure surveys in the

test section of a pilot model for a new facility at the Ames Research Center i

are presented..

. 17. _ W_b _Sullm_ I_ ,a_ho_,_| tO. Oin'timskm

Transonic flow I Unlimited

, CLrcular stagnation chamber i

Rectangular test section STAR Category- 02

le. sm_v cm_.,of.mmru I_ am._c_mt ,_. rapt

Unclassified Unclasslfled__ 35 3 75

"For saleby the National Technical Information Service, Springfield, Virginia 22161

A DESIGN METHOD FOR ENTRANCE SECTIONS OF TRANSONIC

WIND TUNNELS WITH RECTANGULAR CROSS SECTIONS

By Lionel L. Levy, Jr. and John B. McDevitt

Ames Research Center

Moffett Field, Calif 94035

ABSTRACT

A technique has been developed to design entrance sections for transonic or high-speed sub-sonic wind tunnels with rectangular cross sections which satisfies two important requirements:(1) the transition from a circular cross-section settling chamber to a rectangular test section isaccomplished smoothly so as not to introduce secondary flows (vortices or boundaryqayer separa-tion) into a uniform test stream and (2) the transition is accomplished within a specified length. Themathematical technique for shaping the entrance section is described and the results of static-pressure measurements in the transition region and of static- and total-pressure surveys

• in the test section of a pilot model for a new facility at the Ames Research Center arepresented.

INTRODUCTION

A High Reynolds Number Channel is currently operating at the Ames Research Center.It is being used to eonduct experimental studies, over a wide range of Reynolds numbers,that are specifically designed to provide information relevant to the development and evaluation oladvanced computer codes for numerically simulating transonic flows. A schematic of the facility isshown in figure 1. The tunnel, with various test channels of approximately 0.1 square meter (one .square-foot) cross-sectional area, will provide transonic air flows with Reynolds numbers per meterranging from 3XI06 to 120XI06

A schematic of the settling chamber, entrance section, and the first test channel to beemployed tdesigned for tests of airfoil sections at high subsonic Mach numbers) is showp in figure 2.A tech,_ique used to design the entrance section that involves a transition from the circular cross

i section of the settling chamber to the rectangular cross section of the test section is described in thispaper. Also included are the results of static- and total-pressure surveys made in a pilot model(40 percent scale) of the entrance and test sections for the new facility

ENTRANCE-SECTION DESIGN METHODt

The problem of designing a general three-dimensional wind-tunnel entrance section of finite• length has not been solved analytically, in reference 1, Tsien obtained a series solution to the

axisymmetric incompressible irrotational flow equations for an infinite conical-shaped entrance

1976003957-003

section. The coefficients of the series were evaluated using derivatives of a specified velocity distri-bution along the axis. In reference ? Thwaites obtained a series solution to the same equatinns forpotential flow between two equipotential planes normal to the axis. The length and entrance- andexit-radii of the entrance section can bc specified and the cocfficicnts of the series evaluated bysatisfying either of two conditions. One choice insures as uniform a velocity as possible across theentrance of the section; the other insures a monotonically increasing velocity distriblztion along thewalls. While both of these characteristics of the flow are hibhly desirable, they cannot be achievedsimultaneously using either choice for evaluating the series coefficients, at least not for a practical,finite number of terms.

The present design method combines certain features from references 1 and 2. The infinite-length solution of Tsien is examined to establish a set of "control points" (dimensions) to insure amonotonically increasing velocity in the high-velocity portion of the entrance section. Thwattes'finite-length solution is then found so that it passes through these control points and insures asuniform a velocity as possible across the entrance section. The restdting solution is tailored to aspecified entrance-section length to obtain the axial area distribution. A smooth transition from acircular to a rectangular cross section is effected by maintaining the predetermined area distri0utionand satisfying specified slopes.

Control Points from Tsien's Axisymmetric Solution

Tsien's solution, which is used in the present case as a guide for specifying the contractionratio and length of the high-speed portion of the entrance cGne, is graphically summarized ,nfigure 3. The streamlines for which the velocity exceeds the final exit value are shown as dashedlines (streamlines "E" and "F"). Thus, the contraction cone should be designed for a wall shapeinside of streamline E in order to insure that the velocity does not overshoot near the wall. For all

the streamlines, r(x), shown in figure 3(b), r(O)/r(2)',¢ 1.34, which corresponds to a contractionratio of A(0VA(2) _ 1.8. For the present design, a contraction ratio of 2, and axial length of 3 r(2)(corresponding to a streamline between B & C of fig. 3) were chosen for the high-speed portion ofthe entrance section. This conservative apprcach (a wall streamline well within E) was prompted bya consideration of compressibility effects (ref. 3).

The foregoing choice of area ratio and axial distance establishes two control points for thehigh-velocity end of the entrance section, points A and B in figure 4. A streamline that has amonotonically increasing velocity is desired which passes through these points and joins smoothly

with the settling-chamber wall within some practical maximum length, Lmax, predetermined byavailable space. Several satisfactory solutions may be possible as indicated by the dashed lines iqfigure 4. This problem is similar to that solved by Thwaites (ref. 2) in which the entrance_ectionlength and contraction ratio are given and a shape determined. A brief description of Thwaites'method and its application to the present problem are presented next.

Thwaites' Axisymmetric Solution Fit to Control Points

The velocity potential that Thwaites gives is rewritten in a scaled form that is useful indesigning a wind-tunnel entrance section with a specified length and end radii. Thus, with referenceto sketch (a),

a.,

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1976003957-004

' ! ! ,1 l J 'L[ , t

r,V

i , _ -- i R (-L)

: ' 101

-L 0 _ _,u

Sketch (a)

L{ (L) _ ak (kL) (kL)}¢(x,r) = ao + _ sin Io ( I )k=l

where L is the entrance-section length, !o is the modified Bessel's function of the second kind andorder zero, and x and r are coordinates in the axial and radial directions. The velocity components,u,.v, in these respective directions are given by

00u=_=a o+ akcos _ !o (2)k=i

i" N

"_ a_r E /kL)(kL)v - - ak sin 11 {3)

k= 1

i and the scaled stream function is given byr

(L)_ 0 1 [wr_Z (L)_ ak (kL)(kL / ]

_(x,r)= urdr = _ ao_) + -_ cos It (4)k=l

The boundingstreamlinethrough R(0) andR(-L) in sketch(a) and the natureof the internalflow dependupon the manner in which the ak coefficientsof the seriesareevaluated.Two choicesare available.One insuresasuniform a velocity as possibleacrossthe entranceof the section, theother insuresa monotonicallyincreasingvelocityalongthe wall. For the practicallimit of six termssugllestedin reference2, both desirableflow characteristicscannotbe achievedsimultaneously,inview of earlier considerationsin selectingcontrol pointsA andB (fig. 4), a Thwaites' solutionfor a

, boundingstreamlinethrough thesepoints shouldresult in a monotonicallyincreasingvelocity inthis region. Therefore, rite choiceof conditions for evaluating the coefficients was made whichinsuresasuniform a velocity aspossibleat the entrance(x -- -L). For six termsof the series(N = 6)

• and an arbitrary choice ofal " I,

1976003957-005

1

I

ak= Ck Ik _r t ; k = 2'3'" ""6l1 _, R(-L

where C2 = 5/4, Ca = 5/6, C4 = l/3, Cs = 5/54. and C_ = 7/324.

This choice of coefficients usually results in a small adverse velocity gradient at the entrance which

might cause separation. However, as will be seen later, in this application, the adverse gradient wasavoided.

The stream function is constant along streamlines. Hence, ao is evaluated by equating values ofthe stream function at both ends of the bounding streamline, i.e., _bfor x = 0, r = R(0) is equated

to _bfor x = -L, r = R(-L). It is then possible to evaluate _ along the bounding streamline, _bs-

The coordinates of the bounding streamline, R(x), are found as solutions to

_kb_=2 a_ -- + _ cos it (5)k=!

with -L _ x _ 0 specified. This method of solution was programmed and solved on an IBM 360/67computer.

The first attempt to obtain the bounding streamline used the actual settling-chamber radius,

equivalent t_t _cc!ion rad;.us (based on cross-sectional area) and predetermined Lmax. The resultingsolution, which does not pass through points A and B, is shown in figure 5 as solution 1. Subse-

quent attempts using successively shorter entrance_.ection lengths (Lma x) were also unsuccessfulbecause the curvature of the bounding streamline soon becomes so small near the entrance that the

solution could not be found over the entire length using only six terms of the series.

An alternative approach was chosen. A fictitious length and entrance radius, smaller than the

physical size, was used to find a solution which passed through A and B and only a portion of thatsolution was used with the remainder of the bounding streamline specified by practical physical

constraints. Two such trial results are shown in figure 5 (solutions 2 and 3). Solution 3 passesthrough points A and B. The velocity along the bounding streamline was found to decrease slightlyfrom the entrance to point D and then monotonically increase from point D to point A. At point C,where the streamline slope is minus one, the velocity increases to only about 10 percent of its final

value. Therefore, the Thwaittl' solution was used between points C and A and a 45* conical section,

the dashed line in figure 5. was used ahead of point C to satisfy the physical constraints of Lmaxand settling-c_mber radius.

t!

1976003957-006

With an area distribution now available for an axisymmetric entrance section, the n_xt step isto devise a scheme to permit smooth transition of the flow from the circular-cross-section settlingchamber to the rectangular test section.

Transition from Circular to Rectangular Cross Section

The length defined by points C and A in figure 5 was selected for making the transition from

circular to rectangular cross section. This choice was made since about 90 percent of the total

velocity increase occars in this leneth and since construction is simplified by mating the transitionsection with adjoining sections of constant slope. The complete entrance section, thus defined, isshown in figure 6.

The area distribution in the transition section is given by (see fie. 6)

A(x) .=_R_(x) = w(x)h(x) - (4 - It) r_ (x) ; xl < x < 0 (6)

R(x), dR(x)/dx, w(0), and h(0), and rc(0) are given. The comer radias at the test section entrance,re(0), need not be zero. in fact, it was found that for fixed values of w(0) and h(0), the degree ofsmoothness of the transition at the high-velocity end is dependent critically upon the value of re(0).The final cho:,ce of values for w(0), h(0), and re(0) determines the value of R(0) used in theThwaites' solution (see eq. (6) for x -- 9).

The side walls of the transition are described by a five-term polynomial whose coefficients aredetermined by satisfying five boundary conditions. For example, for the half height

h(x)/2=ho +hlx+h2x= +hixi+hjxJ ; x I <x<0 (7_

with boundary conditions I

1. at x = 0 h(x)/2= h(0)/2

I2. atx=0 dh--_'_-Odx

3. atx--xl hlx)/2=Rlxl) 18)

i 4. atx=x, dx = dx xl

d2h(x)125. atx=x_ dxz =0

Boundary condition S is imposed to insure that h(x)/2 varies monotonically. The exponents of thelast two terms of eq. (7) are generalized as i and j so they may be changed to improve the degree of

5

1976003957-007

smoothness of the walls and minimize the deviation of h(y)/2 from R(x). Application of theboundary conditions, eqs. (85, yields for the coefficients of eq. (7).

11o-- h(O)12

hi =0

ij[(i- l)(j- 2)-(i- 2)0- l_][2R(xl)-h(O_!h2 "

(i - 2)(j - i)(j - 2)x_

dR¢'-.) t[(i+ i)(i-2)j(j-1)-i(i-l)lj+ i)(j-2)lxi _ x_+

(i - 250 - i)tj - 2)x,2 tg)

dR(x) }

-j[2R(xj)-h(0)] +(j+ I)x, _ Ix_hi

(i- 25ci-i)x

i[2R(xi)-b(Ol] -(i+ i)xl _ xlhi =2

0- 2)o-i5

Note from the denominatorsof eqs.(9) that i must be greater than 2 and j > i. Similar expressioasfor the half width are obtained by replacing h by w and i, j by m, n, respectively, in eqs. (7) through(9).

Finally, the comer radius distribution, re(X), is determined from eq. (65. The entire transitionprocedure was programmed for the IBM 360/67 computer and combined with the programmedsolution of Thwaites.

PILOT FACILITY AND TESTS

The above method was used to design the entrance section for a High Reynolds NumberChannel at the Ames Research Center. To determine that file method does, in fact,provide smooth Uansition of the flow from a circular to a rectangular cross section, a 0.4-scalemodel of the entrance section and half of the test-section length of the actual channel was built andtested. This model is subsequently referred to as the pilot facility.

Computer inputs used to design the transition section of the pilot facility {after several itera-tiom) are given in table i. The resulting axisymmetric radius distribution for the transition sectionis tabulated in table 2 and plotted in figure 7. Also shovm in figure 7 are the distributions w(x)/2.h(x)/2, and re(X)/2.

6

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1976003957-008

' T ' 1 T, 1 T

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Facility

A photograph of the pilot facility is shown in figure 8. The downstream end of the test sectionis mounted on a gate valve, which, in turn, is mounted on a vacuum chamber. Figure 9 is asketch showing the pertinent details of the pilot facility. At station x = 0, the corner radius of theentrance section is re(0) = 0.762 cm. To facilitate construction of the test section, the comers werewedge shaped as indicated in figure 9. The wedges were sized to provide the same cross-sectionalarea had corner radii been used. This required some hand fairing at, and downstream of, stationx-0.

Locations of static-pressure orifices are also indicated in figure 9. The orific_'s in the transitionsection and the top and bottom walls of tee test section were permanent. Eight orifices werelocated circumferentially in the transition cross section only at x = -10.16 and -22.86 cm. At allother negative x-stations, orifices were located at only the top, side, and radius location of onequadrant. The orifices in the side walls of the test section were mounted in removable plugs whichcould be replaced with a pressure-survey probe that completely spanned the test section. The probeorifice was 5.24-cm ahead of the probe support.

The nominal free-stream Mach number was controlled by choke inserts (of appropriate thick-hess) at the downstream end of the test section (see fig. 9).

rests

Tests were made at atmospheric total pressure fo,- free-stream test-section nominal Machnumbers of 0.6, 0.7, 0.8, and 0.9. Static and total pressure _urveys were made, one location at atime, with separate probes rather than with a pitot-static prot, e. The probes were specially designedto minimize errors due to compressibility effects (local shock waves) st the higher Maeh numbers.

Pressures where sensed by a standard pressure transducer used in conjunction with a "scani-valve." The output signal from each orifice was recorded on magnetic tape and a computer profp_mwas used to convert the records to absolute pressure. The ratios of static to total pressures wereused to obtain Mach number as incl!cated in reference 4.

Because the full-scale facility employs screens in the stagnation chamber (see fig. 2) most ofthe data were obtained with t screen over the entrance section. To evaluate the effects of the

, screen, data were alto obtained with no green.

A minimum number of tests were made using a surface oil-flow technique to es, ablish localflow direction and demonstrate the lack. or existence, of secondary flows near the walh (boundary-layer separation).

7

1976003957-009

I 1 T: !

RESULTS AND DISCUSSION

Results are presented in a manner to evaluate the degree of uniformity of flow m the pilotfacility. Longitudinal Mach number distributions are presented for the complete facility (entrancesection and test section); transverse distributions of Maci, number in the test section are presented.Also presented are the results of total pressure surveys in the test section and oil-film studies whichwere made to determine the existence, if any, of secondary flows.

Mach Number Distributions

Longitudipal surveys - The Mach number distribution in the longitudinal direction (x) of thepilot facility is presented in figure 10 for test-section nominal free-stream Mach numbers, M.

non1 •

of 0.6, 0.7, 0.8, and 0.9. The Mach numbers obtained from wall static pressures are shown by opensymbols for the empty channel, and for the channel with the probe in its most downstream location(x = ! 9.84 cm, v = z = 0 cm). Each data point is the average of the Mach numbers calculated usingpressures measured at several circumferential locations (see fig. (977. The deviation of the individu:..!circumferential values of Mach number from the average was, in the worst case, ±2 percent and inmost cases was less than +! percent. The reduction in Mach number due to the blockage of theprobe support is obvious. The filled symbols represent the Mach number determined from staticpressure measurements at the centerline of the test section with the probe support at the x-stationindicated. There is excellent agreement downstream of the test section entrance between the Machnumbers determined from stream- and wall-static pressure measurements with the probe support :,tx = ! 9.84 cm. The data show the existence of a longitudinal gradient in Mach number in the testsection which is attributed to boundary-layer growth along the walls. (in the full-scale facility thetop and bottom test-section walls are hinged upstream and designed as converging-diverging walls _,,provide a means for minimizing longitudinal gradients.) Comparing the exl_erimental channel-emptydata with the theoretical estimates u. _,:;reference 4, it is seen that the agreement is much better atthe lowest nominal Mach number and at the low-velocity end of the entrance sectton for allnominal Math numbers. This is consistent with the fact that viscous effects become more sigmficantas the Math number and area ratio A(x)/A* (A* is the throat area) approach unity.

Transverse surveys - Typical distributions or Math number in the test section in planes normalto the channel longitudinal axis are presented in figures ! I through 14. Figure I I shows the distri-butions at the test-section entrance (x =0) for the free-stream nominal Math numb_:r.

M..nom = 0.8. These data show a higher velocity at the walls than at the centerline. Any reasonable

estimate from these data of an average Mach number at the walls would be greater than thatindicated by the faired curve through the square open-symbol data at x = 0 in figure lO(c). Thissuggests the possibility of a slight adverse pressure gradient at the beginning of the test section, butif this was the case, the magnitude of the gradient was not sufficient to cause boundary-layerseparation or induce secondary flows downstream (as noted later).

The higher velocity at the wall compared to the centerline at the entrance of the te_t section isalso indicated theoretically by the finite4ength axisymmetric solution of Thwaites Cairo seefig. Jib)). The ratio.of the velocity obtained from the Thwaites' solution across the ex,t of thea.xisymmetri¢ entrance to that at the centedin¢ is shown in figure 12. (Note the expanded s=alcs.)

8

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1976003957-010

1 1 l '

' I' I I

Also shown is the Mach number ratio across the test-section entrance in the y and z directions fromfigure ! 1. These data indicate that the flow is less uniform across the test-section entrance in thehorizontal direction (short dimension) than that indicated for an axisymmetric channel, and moreuniform in the vertical direction (long dimension).

The data demonstrate a slight asymmetry (skewness) of t'._eflow, about i .5 percent in the ydirection and less than 0.5 percent in the z-direction. The asymmetries were determined to resultfrom asymmetries inadvertently built into the entrance section. This fact was established by testsmade with the entire pilot facility rotated 180°. The results are shown in figure 13.

The horizontal distributions of Mac.h number across the center of the test section (z = 0) at

stations downstream of x--0 are shown in figure 14 for several values of M.no m. The datademonstrate completely uniform flow across the test section at these locations. This is the reasonfor the excellent agreement between the Mach numbers at these x-locations determined from walland stream static pressures noted earlier (figure I0).

Total PressureDistributionsandOil-Flow Patterns

To determine the possibleexistenceof secondaryflows, total pressure measurementsweremade at the same (and more) locationsin the test section for which free-streamstatic pressuremeasurements were made. The surveys were made to within 0.32 cm of the side walls and 0.49 _.n|of top and bottom walls. The results indicated no vortices in the flow and no boundary-layerseparation at any free-stream Math number. The only losses in total pressure recorded were a _malldrag-loss due to the green and losses near the walls of the test ,.ection in the region of the bound::olayer. The losses for M.nom = 0.8 are shown in figure ! 5 as the ratio of total pressure measured in

the test section to atmospheric total pressure. The scale on the right in figure 15 is included toemphasize the small magnitude of the total-pressure losses as a fraction of a percent of the h),:alfree-stream dynamic pressure.

Flow studies were made using an oil-film technique to establish the direction of the streamlinesof the flow near the walls and to determine the presence, if any, of boundary-layer separation.Residual oil patterns indicated smooth flow (gently curving and straight streaks in the oil patterns)throughout the pilot facility with no apparent regions of boundary-layer separation. Photographs oftypical oil-flow patterns are shown in figure 16. Fiaure 16(a) is a view into the entrance section andalong the top and left-hand wall of the test section. Figure 16(b) is a view of the left-hand wall nearthe beginninI of the Math number choke inserts(small vertical white line at top center of photo-Ipraph). The larller white streaks near the top of the photoaraph are localized reaions of separatedflow which are traceable to discrete imperfections in the surface fairinl st the juncture of theentrance and test sections and are believed not to be the result of any adverse pressure gradientupstream alonll the walls (see fill. 16(8) at upper left-hand comer of juncture). !

•

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1976003957-011

, i It I

CONCLUDING REMARKS

A method has been presented for the design of entrance sections for high_pecd subsomc windtunnels with rectangular test sections. The technique includes a mathematical procedure for _hapm_

o an entrance section of specified length to insure a smooth transition of the flow from the circularcross section of a settling chamber to a rectangu!at test section. The technique was used todesign the entrance see(ion for the High Reynolds Number Channel at the Ames Research Center.A 40-percent scale model of the entrance section and part of the test section of this facihtywas built and te3ted to assess the design method and evaluate the flow in the test section. Initialresults of surface static-pressure measurements in the entrance section, static- and totai-pres-ure

surveys in the test section and oil-flow patterns on all surfaces indicate that a uniform fraw isattained downstream in the rectangular iest section. No vortices were detected in the flow andno boundary-layer separation was detected.

REFERENCES

I. Tsien, Hzue-Shen: On the Design of the Contraction Cone for Wind Tunnel Feb. 1943, pp. 68 70

2. Thwaites, B. A.: On the Deflga of Contritions for Wind Tunnels. National Physical Laboratory, R. & M. 227_.March 1946.

3. Gothetl. B.: Plane and Three-Dimensional Flow a! High Subsonic Speeds.NACA TM - 1105, 1946.

4. Ames Research Staff: Equations, Tables, and Charts for Compressible Flow. NACA Rep. I 135, 1953.

10

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1976003957-012

T T

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; TABLE 1.- COMPUTERINPUTSFOR TRANSITION-SECTIONDESIGN

w(0) I0. !6 cm

h(0) !5.24 cm

rc(0) 0.762 cm

L(fictitious) 61 cm

R(-L) (fictitious) 30.5 cm

i,j II, 13

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1976003957-013

TABLE 2.- AXISYMMETRIC ENTRANCE SECTION (TRANSITION RF(;ION_

-_. cm R(x). cm

0.0 7.01

1.02 7.02

2.03 7.03

3.05 7 06

4.06 7. !05.08 7.16

6.10 7.22

7. i i 7.30

8 13 7.3Q

9.14 7.50

10.16 7.(,2

11.18 7 75

12.19 7.90

! 3.21 8.06

14.22 8.24

15.24 8.44

16.26 q.66

17.27 8.89

18.29 9.15

!9.30 9.43

20.32 9.73i

21.34 10.06

22.35 10.4123.37 10.79

24.38 I 1.21

25.40 11.6626.42 12.14

27.43 ! 2.67

28.45 !3.2429.46 13.86

30.48 14.54

3 i.50 !5.28

32.51 16.1033.53 17.00

34. i 5 17.60IL

12 i "

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1976003957-014

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